A Domain Decomposition Based Parallel Inexact Newton’s Method with Subspace Correction for Incompressible Navier-Stokes Equations

Abstract

There are two major types of approaches for solving the incompressible Navier-Stokes equations. One of them is the so-called projection method, in which the velocity field and the pressure field are solved separately. This method is very efficient, but is difficult to be extended to another multi-physics problem when an appropriate splitting is not available. The other approach is the fully coupled method in which the velocity and pressure fields stay together throughout the computation. The coupled approach can be easily extended to other multiphysics problems, but it requires the solution of some rather difficult linear and nonlinear algebraic systems of equations. The paper focuses on a fully coupled domain decomposition based parallel inexact Newton's method with subspace correction for incompressible Navier-Stokes equations at high Reynolds numbers. The discussion is restricted to the velocity-vorticity formulation of the Navier-Stokes equations, but the idea can be generalized to other multi-physics problems.

Nonlinear Overlapping Domain Decomposition Methods

“…Such jumps may lead to slow convergence or divergence. Some improved versions are given in [6]. In the next section, we combine the ideas of ASPIN and NE into a right preconditioned Newton method.…”